So something like this ;
love a picture! obviously not to scale!!
The problem I can see with this is the swell would always be in the same place - which we know is not correct. You could have another a+b relationship that dictated the overall length of the bat which would then intern change the position of the swell. But that would mean that the swell position would be dictated by a persons height which I am again not so sure on?
Not sure what the width of the bat has to do with it.
Also the weight could dictate the overall edge/spine a+b - dimension.
Streaky